Here is the source code for reader view for FireFox, we can use this to make some best guesses as to why Stack Overflow doesn't quite work. I would imagine similar criteria is used for other reader view implementations.
Criteria used by reader view that conflict with Stack Overflow
A few thing jump out as to why Stack Overflow doesn't work with a reader view.
It uses criteria designed to remove comments from a page.
There are a few criteria such as length of text (300+ characters for max points as likely candidate), use of commas and class names all designed to remove nodes that look like comments.
As reader mode is designed to read blog posts this is obviously favourable, but on Stack Overflow this is likely to remove large sections of the page as candidates as they have lots of low scoring nodes (I mean....who uses commas in comments anyway? They use valuable characters of your character count! hehe).
Reader View doesn't use semantics as an indicator
This one surprised me, but it doesn't look for semantic elements such as <main>, <article> etc. when making decisions.
This wouldn't help Stack Overflow as it stands as they don't use them either but it would have been my immediate thought on how to fix this.
Class names don't help Stack Overflow
However they do look for class names that indicate whether an item is likely to be relevant.
Negative classes (which I believe include partial matches such as "main-comments" for "comment") are as follows (which are likely to result in a node being removed from the likely candidates list):-
unlikelyCandidates: /-ad-|ai2html|banner|breadcrumbs|combx|comment|community|cover-wrap|disqus|extra|footer|gdpr|header|legends|menu|related|remark|replies|rss|shoutbox|sidebar|skyscraper|social|sponsor|supplemental|ad-break|agegate|pagination|pager|popup|yom-remote/i,
Within that list are "comment" and "share", the comments on a section therefore are likely to score poorly (as they have the class "comment" on each comment) and the actual answer sections are also likely to score poorly due to the "share edit follow close flag" section containing a class of "share".
Stack Overflow could change these class names and that would possibly improve the chances of a full page being rendered in the reader view, but it is a hack and probably not very robust!
Comments and short answers are the killer
As I mentioned length of text in an element and the use of commas are criteria for determining whether an element is a candidate for "the main text" on a page.
Comments, short answers etc. on Stack Overflow will always conflict with this scoring mechanism and so that poses a major problem for Stack Overflow to be able to do anything about reader view compatibility.
With that in mind......
What is the solution?
As far as making a site compatible with reader view, this is not something you should pursue with any vigour, it will lead to poor decisions.
Trying to adjust Stack Overflow to meet the criteria of reader views would result in hacks at best and introducing accessibility issues at worst!
The problem here is that Q&A sites do not behave well with reader views. Try Quora on Reader View, it also doesn't work.
To illustrate my way of thinking on this, the original question could be changed to
"What could FireFox do to its reader view to make it compatible with Q & A sites" and that would then open up discussions about the criteria they use to work out what content to show, as the problem lies with their implementation more than Stack Overflow / Quora (not that Stack Overflow / Quora etc. are perfect by any means!).
Instead I can think of a couple of solutions that would allow the accessibility features I believe you are using reader view for:-
Fix it yourself
As this all seems to have stemmed from the line height changes you could create a plugin or bookmarklet that fixes all the styles on a page.
As the readability source code is available you could easily adjust the source code to account for Stack Overflow specific design (give an extra weighting of +200 points to <div id="mainbar" as that is the container we want to display).
Then just adjust the bookmarklet to point to your own server with the modified readability script and voila, working solution.
If you decide to do this share it with the community, it could get you some nice reputation and would look great on a CV / your social media profiles etc.
Get Stack Overflow to fix it!
A better option would be to ask Stack Overflow to implement accessibility settings. Stack Overflow should try to be a leader in the field and I am sure a request for accessibility features would be well received and eventually added to the development roadmap.
Ask for an accessibility settings screen or drop down. A good starting point would be something like the User Interface Options component.. Click "+ show preferences" and you will see you can adjust a load of things on the site.
This way you could fix the line height (which appears to be the original starting point of this as you use that to adjust the design to your liking). They could also then implement a simplified view similar to reader view ("focused mode").
As an additional benefit of this approach the editor could still be usable and you could view the output in a format that is easy for you to read.
It seems like the best solution and in terms of complexity on a site like SO sits on the low end of technical limitations / design considerations.
Final irony of the reader view criteria system
At time of writing this if you view this page in reader view mode in FireFox you will see the question title and then see my answer as the main body text. Your whole question body text gets removed from the page. I think that happens to sum up the problem perfectly!
